III, Proceed in the same way through all the denominations to the highest; the last quotient with the several remainders annexed, will give the answer sought, and if there be no remainders, the last quotient will be the answer. Ex. 1. Reduce 3138 farthings to the denomination of pounds. 4)3138 In this example we first divide by 4, the number of farthings in a penny; the quotient is 784 pence, and 2 farthings over. The 784 pence are then divided by 12, the number of pence in a shilling. The quotient is 65 shillings and four pence over. Ans. £3 5s 4d 2 far. The 65 shillings are then divided by 20, the number of shillings in a pound, the quotient is £3 and a remainder of 5 shillings. Hence £3 5s 4d 2 far. are equal to 3138 farthings. NOTE. The same rules apply to all the denominate numbers. PROOF OF REDUCTION. 78. After a number has been reduced from a higher denomination to a lower, by the first rule, let it be reduced back by the second, and after a number has been reduced from a lower denomination to a higher, by the second rule, let it be reduced back by the first rule. If the results agree the work is supposed right. Ex. 1. Reduce £15 7s 6d to the denomination of pence. § 74. What is reduction? § 75. Into how many parts is reduction divided? What are they? §76. How do you reduce from a higher denomination to a lower? §77. How do you reduce from a lower denomination to a higher ? 78. How do you prove reduction ? EXAMPLES. 1. In £45 12s 10d how many pence? Ans. 10954. 2. In 87 guineas, how many farthings? Ans. 87696. 3. In 80 guineas how many pounds? Ans. £84. 4. In 1549 farthings how many pounds, shillings, and pence? 5. Reduce 1046 pence to pounds. 6. Reduce 4704 pence to guineas. Ans. 18 guineas, 14s. TROY WEIGHT. $79. Gold, silver, jewels, and liquors, are weighed by this weight. Its denominations are pounds, ounces, pennyweights, and grains. § 79. What things are weighed by Troy weight? What are its denominations? Repeat the Table. EXAMPLES. 1. Reduce 166. 11oz. 15pwt. to pennyweights. 16 lb. 12 oz. in a pound. 192 11 oz. added. 203 20 pwt. in an oz. 4060 15 pwt. added. 4075 pennyweights in 1676. 11oz. 15pwt. 2. In 25lb. 9oz. Opwt. 20gr. how many grains? 3. Reduce 6490gr. to pounds. 24) 6490 Ans. 148340. 20)270 10gr. remainder. 1.. loz. remainder. Ans. 1lb. 1oz. 10pwt. 10gr 4. In 678618 grains how many pounds? Ans. 11776. 9o. 15put. 18gr. Reduce 8794put. to pounds. Ans. 36lb. 7oz. 14put. APOTHECARIES' WEIGHT. 80. This weight is used by apothecaries and physicians in mixing their medicines. Its denominations are pounds, ounces, drams, scruples, and grains. The pound and ounce are the same as the pound and ounce in the Troy weight, the difference between the two weights consists in the different divisions and subdivisions of the ounce. TABLE. 20 grains, gr. make 1 scruple, marked . 3 scruples 1 dram, 1 ounce, 80. What is the use of the Apothecaries' weight? What are its denominations? Of what value are the pound and the ounce? Repeat the Table. EXAMPLES. 1. Reduce 9 83 63 20 12gr. to grains. 9 12 116 ounces. 8 934 drams. 3 2804 scruples. 20 Ans. 56092 grains. 2. Reduce 27 93 63 10 to scruples. Ans. 8011 scruples. Ans. 983 63 29 12gr. 5. Reduce 24033 grains to pounds. Ans. 4 23 03 10 13gr. 6. Reduce 32044 scruples to pounds. Ans. 111b 33 13 19. AVOIRDUPOIS WEIGHT. 81. By this weight are weighed all coarse articles, such as hay, grain, chandlers' wares, and all the metals, excepting gold and silver. Its denominations are tons, hundreds, quarters, pounds, and drams. In this weight the words gross and net are used. Gross is the weight of the goods, with the boxes, casks, or bags, in which they are contained. Net is the weight of the goods only; or what remains after deducting from the gross weight, the weight of the boxes, casks, or bags. A hundred weight is 112 pounds, as appears from the Table. But at the present time, the merchants in our principal cities, buy and sell by the 100 pounds. |